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The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure.
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Feynman-Kac Formulae
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On a likelihood approach for Monte Carlo integration
Z. Tan · 2004
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Another look at rejection sampling through importance sampling
Y. Chen · 2005
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Statistical and Computational Inverse Problems
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Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
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Concentration inequalities
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A computational framework for infinite-dimensional Bayesian inverse problems part i: The linearized case, with application to global seismic inversion
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Conditions for successful data assimilation
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MCMC methods for functions: modifying old algorithms to make them faster
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Lifting the curse of dimensionality
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Learning bounds for kernel regression using effective data dimensionality
T. Zhang · 2005
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Pattern recognition and machine learning
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Optimal rates for the regularized least-squares algorithm
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The ratio of the extreme to the sum in a random sequence
P. J. Downey and P. E. Wright · 2007
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Bridging the ensemble kalman and particle filters
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Bayesian recovery of the initial condition for the heat equation
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Two-stage importance sampling with mixture proposals
W. Li, Z. Tan, and R. Chen · 2013
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On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization
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Bayesian inverse problems with non-conjugate priors
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Large deviations and importance sampling for systems of slow-fast motion
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Posterior consistency for Bayesian inverse problems through stability and regression results
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Importance sampling in path space for diffusion processes
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K. Achutegui, D. Crisan, J. Miguez, and G. Rios · 2014
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Preconditioning the prior to overcome saturation in Bayesian inverse problems
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Bayesian posterior contraction rates for linear severely ill-posed inverse problems
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On the stability of sequential Monte Carlo methods in high dimensions
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A stable particle filter in high-dimensions
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Likelihood-informed dimension reduction for nonlinear inverse problems
T. Cui, J. Martin, Y. Marzouk, A. Solonen, and A. Spantini · 2014
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Discrepancy based model selection in statistical inverse problems
S. Lu and P. Mathé · 2014
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The sample size required in importance sampling
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Parameter estimation by implicit sampling
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